About Course

Take your calculus skills to the next level by mastering the most powerful differentiation techniques and unlocking the secrets of transcendental functions. In this intensive mini-course, you’ll learn to combine functions seamlessly using the product and quotient rules, peel back nested layers with the chain rule, and tackle implicitly defined relationships with confidence. You’ll then extend your toolkit to handle every essential transcendental derivative—from exponentials and logarithms to inverse-trig and beyond—arming yourself with the skills to solve richly structured problems in physics, engineering, and advanced mathematics.

What Will You Learn?

  • Combine functions efficiently with the product and quotient rules
  • Peel back nested composites using the chain rule in any context
  • Differentiate implicitly defined curves and solve real-world related-rates problems
  • Handle every exponential and logarithmic derivative, including nonstandard forms
  • Master inverse-trig and other transcendental derivatives for advanced modeling

Course Content

1. Product & Quotient Rules
Learn to find rates of change for both multiplied and divided quantities without always starting from the basic definition. You’ll see why handling each function separately works, practice rules for combining functions in products and ratios, and explore real-world examples where these shortcuts transform messy calculations into clear solutions.

  • 1.1 Deriving & Applying the Product Rule
  • 1.2 Deriving & Applying the Quotient Rule
  • 1.3 Advanced Examples: Products & Quotients Combined

2. The Chain Rule
Learn to differentiate a function that’s wrapped inside another by treating it as a two-step process. You’ll begin with straightforward cases where one simple rule applies inside a second, then work up to scenarios where several layers are nested together. By the end, you’ll instinctively identify which part of the expression is ‘outer’ and which is ‘inner,’ so you can tackle each layer in the right order—no guesswork required

3. Implicit Differentiation
Discover how to uncover rates when variables are tangled together in a single equation. You’ll apply hidden chain-rule steps to relationships given implicitly, solve for the desired rate of change, and see how these methods model real-world “related rates” problems.

4. Differentiating Exponential & Logarithmic Functions
Uncover the rules that govern rapid growth and decay and their inverse patterns. You’ll learn efficient shortcuts for these special cases, see why they behave the way they do, and tackle combined scenarios—like a quantity raised to its own power—with confidence.

5. Inverse-Trig & Other Transcendental Functions
Extend your differentiation toolkit to include inverse circular behaviors and other advanced patterns such as hyperbolic relationships. You’ll learn the intuitive story behind each rule, discover how they follow from simpler processes, and practice applying them to verify consistency with integration.

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